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- Title
Hermitian Solutions of the Quaternion Algebraic Riccati Equations through Zeroing Neural Networks with Application to Quadrotor Control.
- Authors
Jerbi, Houssem; Alshammari, Obaid; Aoun, Sondess Ben; Kchaou, Mourad; Simos, Theodore E.; Mourtas, Spyridon D.; Katsikis, Vasilios N.
- Abstract
The stability of nonlinear systems in the control domain has been extensively studied using different versions of the algebraic Riccati equation (ARE). This leads to the focus of this work: the search for the time-varying quaternion ARE (TQARE) Hermitian solution. The zeroing neural network (ZNN) method, which has shown significant success at solving time-varying problems, is used to do this. We present a novel ZNN model called 'ZQ-ARE' that effectively solves the TQARE by finding only Hermitian solutions. The model works quite effectively, as demonstrated by one application to quadrotor control and three simulation tests. Specifically, in three simulation tests, the ZQ-ARE model finds the TQARE Hermitian solution under various initial conditions, and we also demonstrate that the convergence rate of the solution can be adjusted. Furthermore, we show that adapting the ZQ-ARE solution to the state-dependent Riccati equation (SDRE) technique stabilizes a quadrotor's flight control system faster than the traditional differential-algebraic Riccati equation solution.
- Subjects
RICCATI equation; ALGEBRAIC equations; HERMITIAN forms; STABILITY of nonlinear systems; QUATERNIONS; DIFFERENTIAL-algebraic equations
- Publication
Mathematics (2227-7390), 2024, Vol 12, Issue 1, p15
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math12010015